Cos Graphh

[naved_s9994]

The method I use to sketch the graph that follows (for NON-CAS), is seeming to be a
long method, which is quite time consuming and now a concern, given that we only get 1 hour in the real exam.



How would YOU go about sketching this graph from f:[-pi, pi] --> R, f(x)= 5cos(2(x+pi/3))
How would you find the intercepts at which it crosses the x-axis. 

Any techniques?

Thank-you 

[TrueTears]

Consider the graph of

for

we have several important points, namely:



Now let



Thus for the graph of the 'important' points will be at



Mark these in as a dot on the x axis.

Now the corresponding y values are:



Find the y axis intercept, ie, .

Now we can see the difference in the 'important' points is , so to the 'important' points until you have all the points within the domain and then put in corresponding y value. Then trace over the dots and you are done!

NOTE: vertical translation/dilation won't affect these "important" points.

[bem9]

get the y intercept at (0,-2.5) and make it the endpoints too (pi, -2.5) & (-pi, -2.5)

next take the point 0,5 and translate it across by  pi/3, this is a maximum
add or minus the period to that point until out of the domain to get other maximums

go half way between two maxiumums and there is a minimum at y=-5, also add or minus the period to this to get other minimums

for x ints, they occur halfway between a max and a min, so use that method to find them

join the dots!

[kdgamz]

FInd the period
find the amplitude
sketch it lightly with a pencil
then translate all x intercepts and stationary points accordingly....
to find the end-points just substitute the max and min values of the domain interval
finally find the y intercept

thats how i do it

[naved_s9994]

Consider the graph of

for

we have several important points, namely:



Now let



Thus for the graph of the 'important' points will be at



Mark these in as a dot on the x axis.

Now the corresponding y values are:



Find the y axis intercept, ie, .

Now we can see the difference in the 'important' points is , so to the 'important' points until you have all the points within the domain and then put in corresponding y value. Then trace over the dots and you are done!

NOTE: vertical translation/dilation won't affect these "important" points.

Thanks so much!
Also, can this technique be applied upon sin graphs?

[TrueTears]

Consider the graph of

for

we have several important points, namely:



Now let



Thus for the graph of the 'important' points will be at



Mark these in as a dot on the x axis.

Now the corresponding y values are:



Find the y axis intercept, ie, .

Now we can see the difference in the 'important' points is , so to the 'important' points until you have all the points within the domain and then put in corresponding y value. Then trace over the dots and you are done!

NOTE: vertical translation/dilation won't affect these "important" points.

Thanks so much!
Also, can this technique be applied upon sin graphs?

Sure can.